I picked up this bit of information when planning our trip to Aachen and it was so handy I felt it needed to be passed on. There are many places near Maastricht not accessible by train, Vaals for example, or that require a long and roundabout route, Aachen and Cologne.
Fortunately that’s where the Veolia (Dutch) bus system and Zuid-Limburg Dagkaart/International comes in. These day tickets are good for traveling anywhere in South Limburg including into the naighboring areas of Germany and Beligum for an entire day for just 7 euros. They can even been used on Veolia trains (although not the NS ones). I purchased our tickets ahead of time from the bus office in Maastricht, but you can also get them on board a bus.
It is an especially good idea to travel to Aachen via bus rather than train. The train will cost you more and take twice as long. Instead take Bus 50 from the Maastricht Station. In about an hour you’ll reach Aachen with only one, very quick switch just on the outskirts of the city. The bus takes you to the central Aachen train station, so you won’t end up in some strange out of the way place.